Mathematisches Kolloquium

Prof. Dr. PhD. Jan Lang (Ohio State University)

"The s-numbers, Eigenvalues, and Generalized trigonometric functions"Abstract: The main goal of this talk is to discuss behavior of s-numbers for integral operators of Hardy type and related Sobolev embeddings, together with eigenvalues for corresponding non-linear problems. Generalized trigonometric functions which were first introduced by Lundberg 1879 will play a crucial role and some of their interesting properties will be discussed.22.07.2015, 15:00 Uhr, Raum 125 (Ulmenstraße 69, Haus 3)Kolloquiumsleiter: Prof. Dr. Peter Takac

Abstract: The aim of this talk is to show how stochastic volatility models can be calibrated to real market data. This task is formulated as the optimization problem and several optimization techniques are compared and used in order to minimize the difference between the observed market prices and the model prices. We briefly demonstrate the complexity of the calibration process on the popular Heston model as well as on the recent fractional stochastic volatility model, which is a jump-diffusion model of market dynamics with approximative fractional volatility.The calibration problem is implemented in MATLAB.Jan Pospíšil is a researcher at the Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic. He specializes in stochastic analysis and stochastic differential equations, recently with applications in finance.

"Estimation of the jump size density in a mixed compound process"Abstract: Consider a mixed compound Poisson process, denoted Y. It can be viewed as a compound Poisson process whose intensity is random and independent of the jumps and the Poisson process of the compound Poisson process. In this talk, we study nonparametric estimators of the density of the jumps from the discrete observation of the process Y, by specific deconvolution methods. First, assuming that the random intensity has exponential distribution, we propose two types of estimators depending on the sample size. Risks bounds and adaptive procedures are provided. Then, with no assumption on the distribution of the random intensity, we propose a nonparametric procedure. 19.05.2015, 11:15 Uhr, HS 221 (Ulmenstraße 69, Haus 3)Kolloquiumsleiter: Dr. Johanna Kappus

Prof. Bahram Hemmateenejad (University Shiraz, Iran)

"Rostock-Shiraz Collaborations: Analysis of the spectrophotometric equilibrium data and potential step-chronoamperometric electrochemical data by matrix factorization and complementary and coupling theorems"Abstract: Multivariate curve resolution analysis of the data recorded in analytical instruments is always associated with problems of rotational and intensity ambiguities. Therefore, these kinds of data analysis methods usually do not converge to a unique solution and hence a range of acceptable solutions are suggested. However, in some instances, when we would like to compare events of close chemical characteristics unique solutions are necessary. Very recently, Neymeyr and Sawall suggested using of complementary and coupling theorems to obtain unique solutions for three-component systems.Last year, a collaboration was started between my research group at Shiraz University and Professor Neymeyr Research group at Rostock University to implement these theorems in two real chemical systems needs unique solutions: Spectroscopic monitoring of solute-induced changes of solvent structure. Beside to the well-known effects of solvent on solute properties, attentions have now been directed toward understanding the effects of solute on the structure of solvent using spectroscopic data analyzed by multivariate curve resolution methods. However, these effects are very smalls and thus very small differences are observed. So, if no unique solution is achieved, there would be an overlap between the ranges of the solutions. In the first part of my talk, I will explain how the method of Neymeyr and Sawall help to study of the effects of different solutes on the structure of methanol-water aggregation.In the second part of my talk, the application of the Neymeyr and Sawall method to analyze potential step-chronoamperometric electrochemical data will be presented. These kind of electrochemical data are three-component systems with inter-correlative components. So, they usually associated with large rotational ambiguity and need special care when they are subject to curve resolution analysis.13.03.2015, 10:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)Kolloquiumsleiter: Prof. Dr. Klaus Neymeyr

Prof. Dr. Irene Benedetti (Universita degli Studi di Perugia)

"Nonlocal multivalued problems in abstract spaces"Abstract: The interest for multivalued equations in abstract spaces is motivated by the study of control problems for partial differential equations. Moreover, nonlocal boundary conditions, such as mean value and multi-point conditions, are particularly suitable to model problems arising in physics. The existence of solutions for these problems is frequently studied with topological techniques based on fixed point theorems for a suitable solution operator. This requires strong compactness conditions, which are very hard to check in an infinite dimensional framework. In this talk will be presented three approaches that weaken the compactness conditions usually required.A first technique is based on the concept of measure of non-compactness combined with a topological degree theory. Alternatively, weak topologies can be exploited, joined with the classical Ky Fan Fixed Point Theorem. Finally, one can consider the multivalued problems in a Hilbert space compactly embedded into a Banach space, in connection with Hartmann-type conditions. Several examples of partial differential equations applying the described three approaches will be shown.

"Kent distributions on Stiefel Manifolds"Abstract: The von Mises-Fisher distribution on the unit sphere is a widely used statistical model for observations on the unit sphere. A limitation in many applications is that it can not model depatures from rotational symmetry about the mean direction. Kent (1982) proposed a 5-parameter distribution on the unit sphere in R^3 which includes the von Mises-Fisher distribution as a subfamily and has ellipse-like contours of constant density. After reviewing relevant distributions on the unit sphere, the talk will discuss the analogous problem on Stiefel manifolds and explain how similar ideas can be used to construct Kent-like distributions in this setting. 12.02.2015, 11:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)Kolloquiumsleiter: Prof. Dr. Wolf - Dieter Richter